doc-src/TutorialI/Inductive/inductive.tex
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     1 \chapter{Inductively Defined Sets}
     1 \chapter{Inductively Defined Sets}
       
     2 \index{inductive definition|(}
       
     3 \index{*inductive|(}
       
     4 
       
     5 This chapter is dedicated to the most important definition principle after
       
     6 recursive functions and datatypes: inductively defined sets.
       
     7 
       
     8 We start with a simple example \ldots . A slightly more complicated example, the
       
     9 reflexive transitive closure, is the subject of {\S}\ref{sec:rtc}. In particular,
       
    10 some standard induction heuristics are discussed. To demonstrate the
       
    11 versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study
       
    12 from the realm of context-free grammars. The chapter closes with a discussion
       
    13 of advanced forms of inductive definitions.
     2 
    14 
     3 \input{Inductive/document/Star}
    15 \input{Inductive/document/Star}
     4 \input{Inductive/document/AB}
    16 \input{Inductive/document/AB}
       
    17 
       
    18 \index{inductive definition|)}
       
    19 \index{*inductive|)}
       
    20 
       
    21 \section{Advanced inductive definitions}